The case of the chicken brake

Once, when riding down Ute Pass toward Manitou Springs, CO, my granddad was discussing runaway trucks whose brakes had failed coming down the pass. At the time, the highway went directly into Manitou Springs, so it was essential to slow down or stop the trucks prior to entering the city with its traffic and pedestrians. Granddad said that some runaway trucks would pull over into the sheer wall of rock that was just to the right of the highway so that the side of the truck would be scraping against the rough rock wall. The friction between the truck and the rock wall would slow the trucks down. This might remind you of the old "truckin" song "Wolf Creek Pass" about a runaway truck with a load of chickens sung by C. W. McCall (or Bill Fries, but that's a whole other story).

A 1989 Federal Highway Administration report indicated that in one mountain state, one sixth of the truck accidents were runaway downgrade accidents. In half the runaway events involving trucks weighing more than 60,000 lbs, brake failure due to overheating was said to be the primary cause.

There are now better ways of dealing with runaway trucks. When driving in a downhill lane in the mountains, you may have noticed the single lane roads slanting off to the side and up the mountain. These are "Truck Escape Ramps" (TERs). They generally have a parallel access road and anchor blocks alongside for the use of wreckers. The steep incline of the ramp slows the truck down, serving as a brake for trucks carrying chickens or other cargo. TERs now usually consist of a combination of positive grade and an arrestor bed utilizing deep sand or loose gravel. The arrestor bed increases the rolling resistance acting on the truck, and helps slow it down. Such arrestor beds are also used at the end of airport runways. Rolling resistance 'R' is the ratio Fr/N. 'Fr' is the force required to move a vehicle longitudinally and 'N' is the normal force between the vehicle and the roadway with no braking and the trans-mission disengaged. R is due to the interaction of the tires with the road surface, friction in bearings, etc. Without the sand or gravel, a ramp would have to be much longer and/or steeper in order to provide control. The increased rolling resistance also helps prevent the truck rolling backwards down the ramp after stopping.

The case-of-the-month involves an 18-wheeler that was out of control on a downgrade in the mountains. To avoid a sharp curve, the truck entered a TER with a constant grade G = +9.8% (ratio of vertical rise to horizontal distance) and traveled a distance L=681 up the TER before coming to a stop. The truck weight "W" was 73,264 lbs, and the TER was covered with deep loose pea gravel with a rolling resistance of 25%.

We would like to determine the speed "V" of the truck as it entered the TER. To do so, we equate the kinetic energy "KE" when entering the ramp to the work done by Fr (force times L) and that due to gravity "g" as the truck moves up the ramp and comes to rest (W × vertical distance).

0.5WV2/g=WGL/(1+G2)½+WRL/(1+G2)½

This assumes that the effects of aerodynamics and any type of braking are negligible. Solving for V gives a speed of 84 mph. This equation also shows that without the arrestor bed, the truck would have traveled about 4 times farther before stopping. Since the downgrade forces are basically constant, these can be divided by the mass to show that the deceleration is 0.35 g's. This will hardly ruffle the chickens' feathers, and they won't be scattered all over the mountainside. That the rolling resistance is 18,229 lbs, and the downgrade component of the weight is 7,146 lbs, explains why the truck did not roll backwards down the TER.

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